Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Introduction to additive combinatorics lecture 10.1 --- the structure and properties of Bohr sets.
An important informal idea in additive combinatorics is that of a "structured" set. One example of a class of sets that are rich in additive structure is the class of Bohr sets, which play the role in general finite Abelian groups that subspaces play in the special case of groups of the fo
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Bolzano-Weierstrass Theorem (Direct Proof) In this video, I present a more direct proof of the Bolzano-Weierstrass Theorem, that does not use any facts about monotone subsequences, and instead uses the definition of a supremum. This proof is taken from Real Mathematical Analysis by Pugh,
From playlist Sequences
Kyle Broder -- Recent Developments Concerning the Schwarz Lemma
A lecture I gave at the Beijing International Center for Mathematical Research geometric analysis seminar. The title being Recent Developments Concerning the Schwarz Lemma with applications to the Wu--Yau Theorem. This contains some recent results concerning the Bochner technique for the G
From playlist Research Lectures
Introduction to additive combinatorics lecture 8.7 --- Bohr sets and Bogolyubov's lemma.
Bogolyubov's lemma says that if A is a dense subset of a finite Abelian group, then the set 2A - 2A has a large structured subset. The structure in question is that of a Bohr set, which I define here. If G is the group F_p^n for some small prime p, then it follows that 2A - 2A contains a s
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Gap and index estimates for Yang-Mills connections in 4-d - Matthew Gursky
Variational Methods in Geometry Seminar Topic: Gap and index estimates for Yang-Mills connections in 4-d Speaker: Matthew Gursky Affiliation: University of Notre Dame Date: March 19, 2019 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Topics in Combinatorics lecture 6.2 --- Variants of the Borsuk-Ulam theorem
The Borsuk-Ulam theorem states that if f is a continuous function from S^n to R^n (that is, from the n-sphere to n-dimensional Euclidean space), then there exists x such that f(x) = f(-x). It has many applications, including in combinatorics. In this video I prepare the ground for explaini
From playlist Topics in Combinatorics (Cambridge Part III course)
The Bolzano Weierstraß Theorem
Bolzano-Weierstrass Theorem Welcome to one of the cornerstone theorems in Analysis: The Bolzano-Weierstraß Theorem. It is the culmination of all our hard work on monotone sequences, and we'll use this over and over again in this course. Luckily the proof isn't very difficult, since we've
From playlist Sequences
Dror Varolin - Minicourse - Lecture 5
No Audio Dror Varolin Variations of Holomorphic Hilbert spaces Traditional complex analysis focuses on a single space, like a domain in Euclidean space, or more generally a complex manifold, and studies holomorphic maps on that space, into some target space. The typical target space for
From playlist Maryland Analysis and Geometry Atelier
Modified Logarithmic Sobolev Inequalities: ... (Lecture 3) by Prasad Tetali
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019
Dror Varolin - Minicourse - Lecture 2
Dror Varolin Variations of Holomorphic Hilbert spaces Traditional complex analysis focuses on a single space, like a domain in Euclidean space, or more generally a complex manifold, and studies holomorphic maps on that space, into some target space. The typical target space for a domain i
From playlist Maryland Analysis and Geometry Atelier
Hyperbolic geometry and the proof of Morrison-Kawamata... (Lecture - 01) by Misha Verbitsky
20 March 2017 to 25 March 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions between mathematics and theoretical physics, especially
From playlist Complex Geometry
My Favorite Theorem: The Borsuk-Ulam Theorem
Many thanks for 10k subscribers! Fun video for you from Topology: The Borsuk-Ulam Theorem. One interpretation of this is that on the surface of the earth, there must be some point where it and its antipode (the spot exactly opposite it) have the exact same temperature and pressure. More ge
From playlist Cool Math Series
Homogeneous holomorphic foliations on Kobayashi hyperbolic manifolds by Benjamin Mckay
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 4) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Positive definite kernels on spheres by E K Narayanan
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Number Theorem | Gauss' Theorem
We prove Gauss's Theorem. That is, we prove that the sum of values of the Euler phi function over divisors of n is equal to n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Number Theory
Davide Fermi - Domenico Monaco - Badreddine Benhellal - Léo Morin
* Magnetic perturbations of Aharonov-Bohm and 2-body anyonic Hamiltonians - Davide Fermi * (De)localized Wannier functions for quantum Hall systems - Domenico Monaco * Quantum Con inement induced by Dirac operators with anomalous magnetic - Badreddine Benhellal * Spectral Asymptotics for
From playlist Mathematics of Condensed Matter and Beyond (February 22-25, 2021)
Euler's Theorem - Graph Theory
An introduction to Euler's theorem on drawing a shape with one line.
From playlist Graph Theory